Is this how you would calculate the probability of the first cell's DNA being correct if it was randomly put together?

Question

I see everywhere on google that the first cells ever where prokaryotes. When I google how many base pairs are contained in a prokaryote I find that "The number of nucleotide base pairs in the prokaryotic chromosome ranges from 160,000 to 12.2 million, depending on the species" (link 1).
With this in mind the correct way to calculate the combinations for DNA would be combinations = 4^n, where n would be the number of base pairs correct (link 2)? So using this information we get the the combinations possible using the lowest number of base pairs would be 4^160,000, for the highest it would be 4^12,200,000 combinations.

So, using all of that and basic statistics (preferred outcomes / total outcomes) the probability of the first cells DNA being what it was would be in the range of 1 / (4^160,000) to 1 / (4^12,200,000). Now I know that there is not only one valid DNA or RNA sequence for life, but if there where 10,000,000,000 valid sequence the probability would still be in the range of 1 / (4^159,990) to 1 / (4^12,199,990). Is this correct? And if this is correct would this not effectively show how silly it is to think that cells could come from nothing? I would appreciate any feedback!

(1) https://education.seattlepi.com/list-ways-prokaryotic-eukaryotic-dna-differ-4687.html
(2) https://www.quora.com/Mathematically-speaking-is-it-true-that-number-of-combinations-of-DNA-sequences-which-are-just-based-on-AGCT-will-far-exceed-the-number-of-atoms-in-visible-universe

Answer 1

What you've calculated there is the probability that that EXACT DNA sequence would be the result of a COMPLETELY RANDOM process. Neither one of those assumptions is correct.



There are many, many DNA sequences that would have functioned perfectly well as the initial genome. Anyone with a background in biology will tell you that you can hack and slash at any functional genome to a surprising extent before you run into any problems.



Furthermore, random chance had nothing to do with this. There were selective pressures and reinforcing feedback loops working long before something as complicated as a cell emerged.



Really what you're doing here is what I like to call "argument by big scary meaningless numbers". You're skimming over your justification for these numbers and using how big they are to hide your lack of logical argument.

Answer 2

What's the point of calculating the probability of something that has already happened?

Answer 3

The first object that could self-replicate would likely not be anything that we would define as "life" by today's standards.